which is the desired state exactly. Then we measure the auxiliary register. If \(|0\rangle \)  is the result, then the iteration succeeds and we obtain the desired state. This happens with a probability of \(P_{s}=\parallel T|\phi ^{(t)}\rangle \parallel ^{2}/{\mathbb {C}^{2}M}\) .
This probability can be increased by using amplitude amplification[1]} before making measurement on the auxiliary register.
